Theorem dfvd2an

Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd2an	$$⊢\left(\left(\phi ,\psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-vd1	$$⊢\left(\left(\phi ,\psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi ,\psi \right)\to \chi \right)$$
2		df-vhc2	$$⊢\left(\phi ,\psi \right)\leftrightarrow \left(\phi \wedge \psi \right)$$
3	2	imbi1i	$$⊢\left(\left(\phi ,\psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
4	1 3	bitri	$$⊢\left(\left(\phi ,\psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \chi \right)$$